Answer:
- Distance between car and the deer when the car stopped = 20 m
- The time required for you to stop once you press the brakes = less than 5 s in order not to hit the deer.
Explanation:
Using the equations of motion,
In the 0.5 s reaction time, we need to first calculate how far he has travelled in that time.
a = 0 m/s² (Since the car is travelling at constant velocity)
x = ?
Initial velocity = u = 20 m/s
x = ut + at²/2
x = 20×0.5 + 0 = 10 m
From that moment,
a = - 10 m/s²
u = initial velocity at the start of the deceleration = 10 m/s
v = final velocity = 0 m/s
x = ?
v² = u² + 2ax
0² = 10² + 2(-10)(x)
20x = 100
x = 5 m
Total distance travelled from when the deer stepped onto the road = 10 + 5 = 15 m
Distance between car and the deer when the car stopped = 35 - 15 = 20 m
b) To determine the time required to stop once you step on the brakes
u = 10 m/s
t = ?
v = 0 m/s²
x = distance from when the brake was stepped on to the deer = 35 - 10 = 25 m
x = (u + v)t/2
25 = (10 + 0)t/2
10t = 50
t = 5 s
Meaning the time required to stop once you step on the brakes is less than 5s.
Answer:
2(maximum), -2(minimum), -2(maximum).
Explanation:
V(t)= 2πcos πt--------------------------------------------------------------------------------(1).
Therefore, there is a need to integrate v(t) to get S(t).
S(t)= 2×sinπt + C ------------------------------------------------------------------------------(2).
Applying the condition given, we have s(0)= 0.
S(0)= 2sin ×π(0) + C.
Which means that; 0+C= 0. That is; C=0.
S(t)= 2 sin πt.
The mass moves to its highest positions at time,t=half(1/2=.5) and time,t=2.5.
Take note that; sin(π/2) = sin(5π/2) = 1 .
Also, the mass moves to its lowest position at time,t=(3/2); also, sin(3π/2) = -1.
Therefore, we have that 2 maximum; -2 minimum and -2 maximum.
Answer:
Explanation:
We shall apply concept of Doppler's effect of apparent frequency to this problem . Here observer is moving sometimes towards and sometimes away from the source . When observer moves towards the source , apparent frequency is more than real frequency and when the observer moves away from the source , apparent frequency is less than real frequency . The apparent frequency depends upon velocity of observer . The formula for apparent frequency when observer is going away is as follows .
f = f₀ ( V - v₀ ) / V , f is apparent , f₀ is real frequency , V is velocity of sound and v is velocity of observer .
f will be lowest when v₀ is highest .
velocity of observer is highest when he is at the equilibrium position or at middle point .
So apparent frequency is lowest when observer is at the middle point and going away from the source while swinging to and from before the source of sound .
